congr_of_eventuallyEq — Mathlib

English

If h: f0 =ᶠ[𝓝[s] x] f1 and hx: f1 x = f x, then HasLineDerivWithinAt for f1 follows from that for f.

Русский

Если f0 и f1 совпадают на nhdsWithin s вокруг x и f1(x)=f(x), то существует переход линейной производной внутри.

LaTeX

$$HasLineDerivWithinAt_{\\mathbb{K}}(f_1,f',s,x,v) follows from HasLineDerivWithinAt_{\\mathbb{K}}(f_0,f',s,x,v) given h and hx$$

Lean4

theorem congr_of_eventuallyEq (h : HasLineDerivAt 𝕜 f f' x v) (h₁ : f₁ =ᶠ[𝓝 x] f) : HasLineDerivAt 𝕜 f₁ f' x v :=
  (EventuallyEq.hasLineDerivAt_iff h₁.symm).mp h

Похожие утверждения